Note: the schedule will be updated as the course progresses.

About Maple worksheets: In order to use the worksheets you need to save them to your hard drive first. In most browsers this can be done by right-clicking the link to the worksheet. Once the file is downloaded to your computer you can open it in Maple.

Integers; divisibility; prime numbers; greatest common divisor, Euclid's algorithm and its applications, the Fundamental Theorem of Arithmetic.

Proof of the Fundamental Theorem of Arithmetic; Mersenne primes; congruences and their properties; tests of divisibility.

Maple worksheets for this week:

• Intro01-24.mw - basic calculations with Maple: divisors, gcd etc.
  
• PrimeListing01-24.mw - a procedure printing all primes smaller than a given integer
  

Web pages for this week:

• RSA Factorizating Challenge
  
• The Largest Known Primes
  
• GIMPS - The Great Internet Mersenne Prime Search

Pseudoprimes, Euler's Theorem, orders of units in Z/m.

Maple worksheets for this week:

• Pseudoprimes02-13.mw - calculations of the numbers of primes and pseudoprimes in different ranges of integers

Applications of Euler's Theorem: prime divisors of Mersenne numbers, RSA cryptosystem.

Maple worksheets for this week:

• ModularPowers02-23.mw - illustration of the difference in behavior of power functions in integers and in Z/n which underlies the RSA cryptosystem.

Additional resources on cryptography:

• Breaking the Code - web page of cryptography course from the International University in Bremen; contains slides on public key ciphers and RSA.
• Handbook of Applied Cryptography - available for free downloads.
• Lecture Notes on Cryptography from an MIT course

Integral domains; subrings; ring homomorphisms; ideals; principal ideal domains (PIDs).

Here are some texts on ring theory available on the web:

• Notes by R. Ash (rings and fields are covered in chapters 2 and 3)
• Ring theory by M. Bernstein and J. Gilbey